Question: Omar is 40 years younger than Emily. Eighteen years ago, Emily was 5 times older than Omar. How old is Emily now?
Explanation: We can use the given information to write down two equations that describe the ages of Emily and Omar. Let Emily's current age be $e$ and Omar's current age be $o$ The information in the first sentence can be expressed in the following equation: $e = o + 40$ Eighteen years ago, Emily was $e - 18$ years old, and Omar was $o - 18$ years old. The information in the second sentence can be expressed in the following equation: $e - 18 = 5(o - 18)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $e$ , it might be easiest to solve our first equation for $o$ and substitute it into our second equation. Solving our first equation for $o$ , we get: $o = e - 40$ . Substituting this into our second equation, we get the equation: $e - 18 = 5($ $(e - 40)$ $ -$ $ 18)$ which combines the information about $e$ from both of our original equations. Simplifying the right side of this equation, we get: $e - 18 = 5e - 290$ Solving for $e$ , we get: $4 e = 272$ $e = 68$.